Beyond the distance of the state transition, we found that both local and global features of the network topology were important predictors of control energy. In line with previous work investigating controllability radii [1]}, energy requirements were lower for randomly rewired networks. Both empirical and topological graphs share the common feature of modularity [2]}, which is destroyed in random topological null models [3]}. Prior theoretical work has demonstrated that modularity is one way in which to decrease the energy of control by decreasing the determinant ratio, a quantification of the relationship between the strength and heterogeneity of direct connections from the controlling node to others [4]}. Here we confirmed that the determinant ratio accurately predicted the required energy, while leaving a small amount of variance unexplained. We expected that this unexplained variance could be somewhat accounted for by features of the local network topology surrounding the stimulated node [5]}. Consistent with our expectation, we found that persistent controllability was the only significant predictor of energy across all frequency bands, indicating a specific role of slow modes in these state transitions. The effect was particularly salient in the \(\alpha \) -band, whose role in memory encoding is well-known [6]}, [7]}.
